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＜E-Book＞
Algebraic Groups and Lie Groups with Few Factors / by Alfonso Di Bartolo, Giovanni Falcone, Peter Plaumann, Karl Strambach
(Lecture Notes in Mathematics. ISSN:16179692)

Edition	1st ed. 2008.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2008
Language	English
Size	XVI, 212 p : online resource
Authors	*Di Bartolo, Alfonso author Falcone, Giovanni author Plaumann, Peter author Strambach, Karl author SpringerLink (Online service)
Subjects	LCSH:Group theory LCSH:Algebraic geometry LCSH:Topological groups LCSH:Lie groups LCSH:Nonassociative rings FREE:Group Theory and Generalizations FREE:Algebraic Geometry FREE:Topological Groups and Lie Groups FREE:Non-associative Rings and Algebras
Notes	Prerequisites -- Extensions -- Groups of Extreme Nilpotency Class -- Chains -- Groups with Few Types of Isogenous Factors -- Three-Dimensional Affine Groups -- Normality of Subgroups Algebraic groups are treated in this volume from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups. The main body of the text is devoted to a classification of algebraic groups and Lie groups having only few subgroups or few factor groups of different type. In particular, the diversity of the nature of algebraic groups over fields of positive characteristic and over fields of characteristic zero is emphasized. This is revealed by the plethora of three-dimensional unipotent algebraic groups over a perfect field of positive characteristic, as well as, by many concrete examples which cover an area systematically. In the final section, algebraic groups and Lie groups having many closed normal subgroups are determined HTTP:URL=https://doi.org/10.1007/978-3-540-78584-2

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